On Jan 8, 2009, at 4:02 PM, Patrick Cassidy wrote:
A few points are selected that seem most productive: (1) [pc] >> Alternative theories can be represented in extensions to the
>> foundation ontology
[PH] > That is extremely unlikely, for two reasons. First, no such foundation is likely to exist; second, even if it did, the extensions to it would be mutually inconsistent with one another, so would not all together form a coherent single ontology. We may be using “extension” in a different sense. Extensions in the sense I intend do not have to be logically consistent with each other.
Hmm. OK, then, in what sense is this resulting, er, structure of extensions an ontology? And why are you not just being vacuous here, and urging that there should be many alternative, mutually inconsistent, ontologies? We can arrange for that with a very low cost to the government.
[[PC]] The base FO plus extensions would form a hierarchy of possible ontologies and ontology modules from which parts could be taken for specific applications. Each extension would have to be logically consistent with the sum of modules of which it is a submodule. It will be essential to specify which branches of the hierarchy are logically inconsistent with which others. Having done that, it will be possible to take and combine modules with some confidence that the whole will be logically consistent. Proving consistency among specific modules may well be intractable, but some degree of certainty may be derived by running a consistency checker for some time (or, being open-source, having everyone interested run a consistency checker on the parts of interest to them, perhaps using SETI-like system for distribution of tasks and receipt of results) . Such a hierarchy will allow a much higher level of confidence in the consistency of any given collection of modules than an unregulated collection. Any two collections of modules known to be consistent, or not proven to be inconsistent, should then be able to be automatically merged into a common ontology that should also be consistent, and able to produce the same inferences form the same data as the individual collections used locally. Using this hierarchy (and creating any local extensions desired, based on the terms in the extracted modules) would provide what I would consider a higher level of interoperability than any I have seen suggested by any technique other than everyone using the same ontology. Not every ontology describable using the terms of the FO would necessarily be consistent with the FO (one only has to assert (not P) for some P in the FO), and therefore would not be part of this hierarchy. Ontologies described in terms of, but inconsistent with, the base FO might be maintained in a separate registry. That will be an issue for decision by the committee maintaining the FO.
Well, now, this is certainly a reasonable grand vision to guide future effort and research. What you describe here is very similar to what John Sowa has described as a lattice of theories, and what Cyc has implemented using its 'micro-theory' context mechanism. (Cyc actually has the choice of modules semi-automated, as part of the overall Cyc ontology is a fairly comprehensive ontology of contexts themselves, allowing the inference engine to reason about what assemblages of micro-theories are most suitable for various reasoning tasks or topic areas.)
But allow me to suggest one small amendment. Given the notions of being able to combine mutually consistent modules, why do we need to have a single 'basic' FO at all? This combining-module idea does not depend on there being a single central 'basic' module somewhere in the lattice, or on all concepts being reducible to a smallish set of 'primitives'. It can be a true catalog of various alternatives, with no single 'root', and still provide the interoperability advantages. I have no problem with the lattice of theories notion: it is this mythical single primitive core that is so unconvincing: but your vision here does not seem to depend on that. For example, for some purposes, a discrete time and a continuous space ontology seems useful; for others, it is important to allow temporal limit points, but spatial references can be minimal, and so on. Why do we need to decide which combinations are more 'basic' than others, when it seems that all such decisions will be largely matters of taste, and likely fraught with endless controversy?
(3) [PH]> >> This seems vanishingly unlikely. This first requirement forces this common theory >> to be as small as possible, but you believe that it will be as large as any theory >> every conceived by the human mind.
[PC] >> No, the theory encoded by the FO is only as large as the number of primitives and their deductive closure. But extensions can be infinitely large, since there is no limit to the number of complex concept representations that can be constructed as combinations of the primitive concept representations.
[PH] > Since these complex concepts are all defined, they are all eliminable. The extensions have the same expressive power as the FO. So the FO itself already has the expressive power of every other theory.
[[PC]] Well, if “largeness” is the same as “expressive power” in your terminology, then, yes. I am accustomed to thinking of size as something different.
The point is that this single theory has to be both small, and expressive enough to define all concepts adequate for human thought. There is no reason to suppose that such a theory exists, and many reasons to suggest otherwise. And, perhaps more to the current point, its not even clear that it would be very much use even if it did exist, cf. above.
(4) [PC] >> I recall that PH and I had a long exchange last year or so at the end of which I thought that we agreed that 4D and 3D assertions could be translated into each other. Did I get a wrong impression, or is PH misinterpreting what I am saying?
[PH] > You got a wrong impression. But the point is not just about translation. I recently had a discussion with Barry Smith about this. Barry's view of the way to reconcile 3-D with 4-D (apologies for the terminology) is that the 4D perspective simply classifies everything as an occurrent. That is the most natural way to express it from his perspective, and it is in a sense accurate. For Barry, people are continuants, and the 4D-ers say they are occurrents: a simple difference of ontological opinion, like me saying I'm Irish and Barry saying I'm American.
> That would be one way to reconcile the two point of view, but it has the demerit that if the basic ontology accepts the distinction, there have to be two 'me's: the occurrent and the continuant. And this is a problem for the 4Ders such as myself, because from our point of view, this bifurcation of entities into two halves is an ontological mistake. From this point of view, there simply is no meaningful distinction to be made
between continuants and occurrents; that all
the so-called continuants are in fact occurrents. From this point of view, there is no disagreement between Barry saying I am a continuant and me saying I am an occurrent; we aren't disagreeing about any matter of fact, or indeed about anything.
> The problem lies higher up the classification chain: it is the notion, fundamental to Barry, that the occurrent/continuant distinction is basic ("upper") and also sharply dichotomous, so that nothing can possibly
be in both categories. To me, in contrast, the distinction is vacuous or, at most, amounts merely to a syntactic preference for writing certain time-dependent facts in one style rather than another.
> Now, it is possible to translate between these points of view, but not to reduce them to a single one. They are not two branches extending from a common trunk: they are more like two completely separate plants which are about the same height. They give different accounts
of Pat Hayes the person: in one viewpoint, there are two of me: me the continuant and me (my lifespan) the occurrent, and all the vocabulary for talking about me has to be duplicated. One cannot simply say that the 4D perspective is got by equating these (though that would be intuitively correct) as the ontology itself would prohibit this equation.
[PC] >> If some person PH is classified in one ontology as 4D and in another as 3D, clearly the ontologies cannot be combined under the assumption that the label PH applies to the same thing in the two cases. It isn’t.
[PH] > Ah, but you see, it IS. That is the critical point. Lets agree that I am what I am, the facts of my life are what they are, and so on. Nobody will dispute any of this, let’s suppose. Still, two philosophers can disagree about how all this stuff should be encoded in an ontology. But they are both talking about the same person, the actual Pat Hayes in the actual world. (If they aren't, there is something badly wrong with their ontologies.) The two ontologies conceptualize me differently, but it is simply factually wrong to claim that I am two persons, just because two philosophers disagree about how best to describe me. Everyone agrees that I last for a time and occupy space and have properties which vary with time, and so on. They just disagree about how to formulate this in a logic. But neither of them thinks that there are two Pat Hayeses, and any ontology which says there are is just flat wrong. http://www.ihmc.us/users/phayes/PatHayes
denotes me, the actual me, here in the actual world.
[PC] >> In one case, it is a 4D entity whose lifetime is PH4D and in the other case it is a 4D entity whose lifetime is PH4D, where the ‘lifetime’ is in the FO even if that concept is not in the 3D ontology (actually, I use a “dimension-neutral object” to relate the two). When the ontologies are translated or merged
[PH] > If you merge them, they will be inconsistent. I agree that in many cases one can translate between the two points of view, but its not easy and not always possible at all. I've never seen a program that can do it.
[PC] >> , the different entities PH3D and PH4D are both present, and assertions about the properties of one in 3D-speak can be translated into assertions about the properties of the other in 4D-speak.
[PH] > Yes, though not always in the other direction.
[PC] >> The problem here again appears (from the description) to be an attempt to use the same term to refer to 2 different entities –a terminology clash.
[PC] well, my point is that a 3D entity and it corresponding 4D entity are truly different though intimately related things, though they are labeled by the same term by different people.
The problem goes deeper than this. The things which some philosophers call 'continuants' are not either 3-d or 4-d when viewed from a 4-d perspective; they are simply impossible
. They have to be 3-dimensional but also persist through time, which is logically incoherent in a 4-d ontological perspective. (Continuants aren't the 3-d slices of the 4-d thing; those are different at different times, but continuants retain their identity through time.) Its not just a matter of terminology. One perspective insists that things exist which are provably
impossible when seen from the other perspective. It is possible for a broad-minded 4-d thinker to take what the other guys say and make a kind of sense of it (I speak here from personal experience) but only by 'translating' it a way that the other guys insist isn't acceptable, by denying a basic assumption of their universe.
One philosopher may insist that only 4D entities exist, and another philosopher may insist that only 3D entities exist. These are different **belief systems** about their real world. As far as an ontological engineer should be concerned, what “exists” is only what is or can be represented in an ontology, and ontologically speaking, both 3D and 4D entities exist in that sense.
But not in the same ontology. There is no single consistent ontology that admits both continuants and 4-d histories.
We can model the belief systems of those ontologists, by asserting the “non-existence” in the sense that the philosophers are using, and since both of those belief systems assert the non-existence of something that is in the ontology, then whether these belief systems are or are not inconsistent with the base FO (which has both kinds of entities)
Before proceeding, please show us a sketch of this part of the basic FO, containing both kinds of entity.
depends on how one interprets the philosophers’ view of “exist”. If it is identical to the logical “exists’ applying to axioms in the ontology, there would be an inconsistency, and both belief systems would be inconsistent – moved into a module in the “inconsistent” set. The ontology would still be able to express assertions about the 3D and 4D entities. IF the ontologists’ “exists” is something different – existence in the real world, or in some ideal world, then both theories individually would be consistent with the base FO, though inconsistent with each other. Then they could be put into different logically inconsistent extensions of the FO.
It all sounds very nice, but it doesn't actually work out this way. Just try it and you will find out why.
[PH] > But my point is that there is only one entity, in fact. And it is important for an ontology to be able to say this, and clearly draw appropriate conclusions. If I am in a room and nobody else is in it, there is one person in the room. Not two people, one of them 4-d and one of them 3-d.
From an ontological point of view, I would say there are at least two entities: a PH3D and a time-slice of PH4D.
And how do they differ? Which of them has my social security number? Can one of them be hungry and the other not, a the same time? (Why not?)
In fact, there are an infinite number of time slices of PH4D, though one is likely to be concerned only with one of them.
(5) [PC] >> , The FO needs to be permissive to serve its purpose of translation. Where there are logical inconsistencies, one or both of the candidate entities needs to be moved to an extension (which can be logically incompatible with other extensions). This decision would be taken by a vote of the executive committee for the FO project.
[PH] > I cant help expressing my amusement at the naiveity of this casual remark. Patrick, have you ever been on a standards working group?
I have attended meetings of some groups, and am aware of the difficulty of finding consensus. But a practical project of this kind cannot depend on consensus, there has to be a simple majority up-or-down vote on issues of controversy, and very quickly. Anyone who cannot bear to participate under such conditions doesn’t have to – that will be clear before any organization work gets under way. I expect there will be enough people oriented toward a practical solution to form the large community that is required for this project. If not, the project will never start – no harm done. This isn’t naïve, it’s practical and realistic.
I hope you will agree to be the chairman.
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